Answer:
Phil is 16 inches tall and his shadow is 8 inches tall
Step-by-step explanation:
this is an algebra word problem.
1. <em> Find the unknown and label it x.</em>
Let Phil's shadow be x inches.
2. <em>find other unknown quantities and define them with</em>
Phil's height= 2x (phil is shadow is half as long as Phil is tall)
3. <em>FInd the equation</em>
if he was 4 inches taller (2x+4)
and his shadow was three inches shorter (x-3)
his height ( 2x+4) times the shadow's height (x-3) would be 100 square inches.
(2x+4) ×(x-3)=100
(2x+4)(x-3)=100
this is a quadratic equation and there are a number of ways to solve these. the two main ways are
1. quadratic equation
2. expanding and factorising
3. graphing
we will use 2. expanding and factorising for this problem. We need to make the right hand side = 0 by first factorising then rearranging.
(2x*x)+(2x*-3)+(x*4) +(4*-3)=100
2x^2 -6x+4x-3x-12=100
2x^2 -2x=112
2x^2 -2x-112=0
once factorised take out the common factor of 2
2(x^2-x-56)=0
now factorise what's in the brackets ( two numbers multiply to make 56 but add to make -1.
2(x-8)(x+7)=0
x-8=0 => x=8
x+7=0 x=-7 not possible
the shadow is 8 inces long. Phil is 16 inches tall.
Hope this is of help :)
